The Phelps-Koopmans theorem and optimality

Debraj Ray

    Research output: Contribution to journalArticlepeer-review


    The Phelps-Koopmans theorem states that if every limit point of a path of capital stocks exceeds the "golden rule," then that path is inefficient: there is another feasible path from the same initial stock that provides at least as much consumption at every date and strictly more consumption at some date. I show that in a model with nonconvex technologies and preferences, the theorem is false in a strong sense. Not only can there be efficient paths with capital stocks forever above and bounded away from a unique golden rule, such paths can also be optimal under the infinite discounted sum of a one-period utility function. The paper makes clear, moreover, that this latter criterion is strictly more demanding than the efficiency of a path.

    Original languageEnglish (US)
    Pages (from-to)11-28
    Number of pages18
    JournalInternational Journal of Economic Theory
    Issue number1
    StatePublished - 2010


    • Dynamic optimization
    • Efficiency
    • Nonconvexities
    • Phelps-koopmans theorem

    ASJC Scopus subject areas

    • Economics and Econometrics


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